2. An elevator is idealized as a weight of mass m supported by a spring of stiffness k. If the upper end of the spring begins to move with a steady velocity v, show that the distance u, that the mass has risen in time t is governed by the equation: m + ku' = kvt If the elevator starts from rest, show that the motion is: u' (t) = vt sin wnt Wn Sketch a plot of this result.